TITLE:
Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions
AUTHORS:
Christian Mathew, Yao Fu
KEYWORDS:
Multilayered Composite and Sandwich Plate, Transverse Stress, Continuity Condition, Arbitrary Boundary Condition, Layerwise Theory, Least-Squares Formulation
JOURNAL NAME:
World Journal of Engineering and Technology,
Vol.12 No.1,
January
11,
2024
ABSTRACT: Laminated
composites are widely used in many engineering industries such as aircraft,
spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D
deformations of a multilayered, linear elastic, anisotropic rectangular plate
subjected to arbitrary boundary conditions on one edge and simply supported on
other edge. The rectangular laminate consists of anisotropic and homogeneous
laminae of arbitrary thicknesses. This study presents the elastic analysis of
laminated composite plates subjected to sinusoidal mechanical loading under
arbitrary boundary conditions. Least square finite element solutions for
displacements and stresses are investigated using a mathematical model, called
a state-space model, which allows us to simultaneously solve for these field
variables in the composite structure’s domain and ensure that continuity
conditions are satisfied at layer interfaces. The governing equations are
derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations
and the associated side conditions residuals over the computational domain. The
model is comprised of layerwise variables such as displacements, out-of-plane
stresses, and in- plane strains, treated as independent variables. Numerical results are
presented to demonstrate the response of the laminated composite plates under
various arbitrary boundary conditions using LSFEM and compared with the 3D
elasticity solution available in the literature.